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Unformatted text preview: 6.003 Homework 13 Please do the following problems by Wednesday, May 12, 2010 . your answers: they will NOT be graded. Solutions will be posted. You need not submit Problems 1. Transformation Consider the following transformation from x ( t ) to y ( t ): + x ( t ) y ( t ) p ( t ) cos( t ) w 1 ( t ) w 2 ( t ) w 3 ( t ) where p ( t ) = k = ( t k ). Determine an expression for y ( t ) when x ( t ) = sin( t/ 2) / ( t ). 2. DT processing of CT signals Consider the following system for DT processing of CT signals: H 1 ( j ) H 2 ( e j ) H 3 ( j ) uniform sampler sample-to- impulse x a ( t ) x b ( t ) x c [ n ] y d [ n ] y e ( t ) y f ( t ) where x c [ n ] = x b ( nT ) and y e ( t ) = y d [ n ] ( t nT ) . n = The frequency responses H 1 ( j ) and H 3 ( j ) are given below. 2 T 2 T 3 2 T 3 2 T H 1 ( j ) 1 T T H 3 ( j ) T Part a. Assume in this part that H 2 ( e j ) = 1 for all frequencies...
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